Numerical Method TU Board 2078 question paper

Derive the formula for integration using Simpson's 3/8 rule. Use Secant Method to estimate the root of equation $x^2-4x-10=0$, with initial estimate $x_1=4$ and $x_2=2$.

What do you mean by boundary value problem? Use shooting method, solve the equation: $y^{\prime \prime }=6x^2$, with $y(0)=1$ and $y(1)=2$ in the interval $(0,1)$ for $y(0.5)$ taking $h=0.5$.

Write an algorithm and program to compute the interpolation using Lagrange Interpolation.

Show that the rate of convergence of Newton's Raphson method is quadratic.

The temperature of a metal strip was measured at various time intervals during heating and the values are given in the table below. Time('t' min)1234Temp('T' °C)7083100124If the relation between the time 't' and temperature 'T' is of the form: $T=b{e}^{t/4}+a$. Estimate the temperature at $t=6$ minute.

Given the following set of data points. Obtain the table of divided difference and use that table to estimate the value of $f(1.5)$. x12345$f(x)=x^3-1$072663124

Solve the following system of linear equation by Gauss Elimination with Pivoting. $2x+2y+z=6$ $4x+2y+3z=4$ $x-y+1=0$

Determine the Eigen Values and corresponding Eigen Vectors for the matrix. $$A=\left[\begin{array}{ccc}1& 6& 1\\ 1& 2& 0\\ 0& 0& 3\end{array}\right]$$

The table below gives the values of distance travelled by a car at various time intervals during the initial running. Time('t' sec)56789Temp('T' °C)10.014.519.525.532.0Estimate the velocity and acceleration at time $t=7$ sec.

Solve the following integral using trapezoidal rule for $n=8$. $$I={\int }_2^4(x^4+1)dx$$

Given the equation $y^{\prime }=3x^2+1$ with $y(1)=2$, estimate $y(2)$ by Euler's Method using $h=0.2$.

Solve the Poisson's Equation ${\nabla }^{2}f=2x^2{y}^2$ over the square domain $0\le x\le 3$ and $0\le y\le 3$ with $f=0$ on the boundary and $h=1$.